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now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | what exactly is the `` iron curtain '' that sir winston churchill described ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | you could almost view it as united states influence , a united states colony , they had so much influence with batista . and in the case of vietnam , it was a french colony . so you can imagine , in all of these situations the existing rulers were not that popular . | was the pattern similar in case if iraq invasion ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | and every time , it ended up in either a us defeat or a stalemate . take whatever lessons there are from this , but it is a kind of an interesting pattern that had happened multiple times , pretty much every engagement that we had during the cold war . | how did the cold war come to an end ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | and every time , it ended up in either a us defeat or a stalemate . take whatever lessons there are from this , but it is a kind of an interesting pattern that had happened multiple times , pretty much every engagement that we had during the cold war . | how did the cold war end ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | in the case of cuba , you have people like fidel castro . in vietnam you have people like ho chi minh . and then korea is a little bit different , because you did have a communist nationalist independence movement , but kim il-sung was n't necessarily the leader of that movement . | who were kim-il-sung and ho-chi-mihn ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | in the case of cuba , you have people like fidel castro . in vietnam you have people like ho chi minh . and then korea is a little bit different , because you did have a communist nationalist independence movement , but kim il-sung was n't necessarily the leader of that movement . | trivia question : what was ho chi minh 's real name ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | and you could also imagine , there were many capitalists in the united states , who for their own selfish reasons , were afraid of capitalism spreading to the united states , because maybe their wealth would be redistributed . but regardless of what the justification , whether it was a more noble wanting people to have... | what did the soviet union really want to do after they fell ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | they kind of marginalized them , and installed kim il-sung probably because he was more aligned with them , but he was communist . now the reality is , these guys come in under these very egalitarian , equality for all , let 's get retribution for the wrongs that were done to us before , but probably all of them start ... | why did the guys who ran the soviet union let all the places declare independance ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | some of the vietnamese who really were aligned with the french , probably got extra favors , and so their wealth was n't necessarily due to innovation or competence , but really just where they fit into the political order . maybe some other people did have legitimate wealth . so you imagine , when any of these type of... | what is the objective `` legitimacy '' for someone 's wealth ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | but this is just the general pattern that happened every time . and every time , it ended up in either a us defeat or a stalemate . take whatever lessons there are from this , but it is a kind of an interesting pattern that had happened multiple times , pretty much every engagement that we had during the cold war . | then what made soviet union fall which ended of the cold war ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | so you have to take everything with a grain of salt . and even in this video , i 'll talk about , maybe , some patterns , or some themes , that i 've seen , do n't take that as just the truth . think about it for yourself , if it makes sense , it makes sense . | is it true that ww1 ww2 and the cold war were all caused by the assassination of a prince i did n't even learn about in school ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | so the general pattern across all of these , is that before the us got involved , and before a communist-leaning regime got involved , these were all , in some ways , subjugated populations . in korea , it was subjugated by the japanese . it was a japanese colony . | wait korea was controlled by the japanese ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | you could imagine it 's a very popular notion to run on , and depending on how true it is . but it 's a very popular notion to run on , to tell people , look , you 've seen all of these people who 've gotten questionable wealth , and maybe , some of these people who got questionable wealth got it by being aligned with ... | are the people of the communist countries better off than if they were living here ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | but this is just the general pattern that happened every time . and every time , it ended up in either a us defeat or a stalemate . take whatever lessons there are from this , but it is a kind of an interesting pattern that had happened multiple times , pretty much every engagement that we had during the cold war . | why was the us acting as the enemy and what made russia look at them that way ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | why do n't we do that with this person here and redistribute that wealth to the rest of society ? and if you 're looking for a political ideology that seems to fit with this idea of trying to correct things that maybe looked wrong during the colonial or the subjugated rule , communism seems to fit that . it 's kind of ... | why was america sort of the '' bad guy '' or so it seems ? |
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt... | and every time , it ended up in either a us defeat or a stalemate . take whatever lessons there are from this , but it is a kind of an interesting pattern that had happened multiple times , pretty much every engagement that we had during the cold war . | why did massive conflict continue to erupt ( wwi , wwii , cold war , decolonization ) ; why did violent conflict keep recurring during the 1900s ? |
hi , this is becca from khan academy , and today i 'm going to be talking about temperance . so , what was the temperance movement ? in this video , i 'll talk a little bit about what temperance was , what its causes were , and how it started to develop in the early-1800s . temperance was the idea that americans drank... | hi , this is becca from khan academy , and today i 'm going to be talking about temperance . so , what was the temperance movement ? in this video , i 'll talk a little bit about what temperance was , what its causes were , and how it started to develop in the early-1800s . | was emily dickenson in the temperance movement ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there . | why does 5^-2 becomes 1/25 and not -25 like how 5^2 becomes 25 ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there . | ca n't 5^-2 become -25 or is it the fact that because 2 is negative that you have to follow the law of indices ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | this will be my y values . let 's start first with something reasonably negative but not too negative . so let 's say we start with x is equal to negative 2 . | can anyone explain to me why a negative power is always a fraction ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ... | when do exponential functions come in the real world ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | it 's not going to be on the x-axis . 1/25 is obviously greater than 0 . it 's going to be really , really , really , really , close . | why does any number to the 0 power always become a 1 ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this curve going , you see it 's just going on this someti... | how would one write the range of a exponential function ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | now let 's think about when x is equal to 0 . then y is going to be equal to 5 to the 0-th power , which we know anything to the 0-th power is going to be equal to 1 . so this is going to be equal to 1 . | why is anything to the zero-th power equal to 1 ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so i have positive values over here . so let me draw it like this . so this could be my x-axis . | can you take the derivatives of functions like that ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so that 's y . this is x . that 's a negative 2 . | when the exponential function follows the equation : a ( b ) ^x , what do the a and b stand for ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | and now we can plot it to see how this actually looks . so let me get some graph paper going here . my x 's go as low as negative 2 , as high as positive 2 . | what part of an equation tells you how steep the graph will be ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | now let 's try another value . what happens when x is equal to negative 1 ? then y is 5 to the negative 1 power , which is the same thing as 1 over 5 to the first power , or just 1/5 . | what happens when i 'm graphing a negative number ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so let 's make that my y-axis . and my x values , this could be negative 2 . actually , make my y-axis keep going . | in the positive function , both x and y values increase i presume , and in the negative the x value increases , while the y value decreases ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there . | how do you find the asymptote of an exponential function , for example , of y=- ( 2^x ) +1 ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | actually , let me make the scale on the y-axis . so let 's make this . so we 're going to go all the way to 25 . | how do you make an exponential function ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so let 's make that my y-axis . and my x values , this could be negative 2 . actually , make my y-axis keep going . | is there a formula , like y=mx+b or y=a ( x-h ) ^2+k ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | 2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite . | how would you draw a cubic graph when given a function ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | then y is 5 to the negative 1 power , which is the same thing as 1 over 5 to the first power , or just 1/5 . now let 's think about when x is equal to 0 . then y is going to be equal to 5 to the 0-th power , which we know anything to the 0-th power is going to be equal to 1 . | so when x = 0 , y= always no matter what one ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | 2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite . | how do you find the exponential function when the graph is given ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | now let 's try another value . what happens when x is equal to negative 1 ? then y is 5 to the negative 1 power , which is the same thing as 1 over 5 to the first power , or just 1/5 . | in y=ab^x , why will b never be a negative number ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | then y is 5 to the first power , which is just equal to 5 . and let 's do one last value over here . let 's see what happens when x is equal to 2 . | also , when exponential functions are graphed , how does one describe the shift/reflection/dilation ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so this is going to be 5 , 10 , 15 , 20 . and then 25 would be right where i wrote the y , give or take . so now let 's plot them . | what would be the domain and range of the problem sal is using ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | my x 's go as low as negative 2 , as high as positive 2 . and then my y 's go all the way from 1/25 all the way to 25 . so i have positive values over here . | is the a way to determine an exponential function given a table ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so that 's y . this is x . that 's a negative 2 . | why do you have to find the x value ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | i 'm slightly above 0 . i 'm increasing above that , increasing above that . and once i get into the positive x 's , then i start really , really shooting up . | what happens if your zero is 100 and is increasing by 10 % , what would you do then ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . | will there be a time when the line on the parabola will be straight ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ... | do all exponential functions have horizontal asymptotes ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | 2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite . | how do you write an exponential function whose graph passes through the given points ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | right at the y-axis , we have y equal 1 . right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . | why i can not select exponential trend line excel where the number of my data equal zero ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so that 's y . this is x . that 's a negative 2 . | how do you graph an exponential function when x is a decimal ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | now let 's do this point here in orange , negative 1 , 1/5 . negative 1/5 -- 1/5 on this scale is still pretty close . it 's pretty close . | if you are given an exponential graph for instance how can you figure out the equation ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | 2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite . | i know how to graph just a parent function but how would you graph a problem when it also has a number in front and the x on the parent function is subtracting a number ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | my x 's go as low as negative 2 , as high as positive 2 . and then my y 's go all the way from 1/25 all the way to 25 . so i have positive values over here . | is it possible to have the line curve all the way over and into a circle if the numbers get big enough ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ... | are exponential functions just a function when the variable is the exponent ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . | how to sum , product , divide or subtract two graphs ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . | how would you find end behavior , domain and range , positive and negative , and increasing and decreasing points ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so then if i just keep this curve going , you see it 's just going on this sometimes called a hockey stick . it just keeps on going up like this at a super fast rate , ever-increasing rate . so you could keep going forever to the left , and you 'd get closer and closer and closer to 0 without quite getting to 0 . | what is the rate of change ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so that is negative 2 , 1/25 . it 's not going to be on the x-axis . 1/25 is obviously greater than 0 . | the line keeps going on forever in the x direction ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | and now we can plot it to see how this actually looks . so let me get some graph paper going here . my x 's go as low as negative 2 , as high as positive 2 . | how would we graph a fraction ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ... | how do you find the domain and range of exponential growth and decay functions ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . | how do you graph something like 5^x+3 ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so this is going to be 5 , 10 , 15 , 20 . and then 25 would be right where i wrote the y , give or take . so now let 's plot them . | what would the horizontal and vertical asymptotes be ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . | also the domain and range ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ... | asymptote for an exponential function ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so that 's y . this is x . that 's a negative 2 . | so you substitute the x value into the exponent ex 3^x ( if x is -8 you just plug it in and solve right ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | and i 'll try to center them around 0 . so this will be my x values . this will be my y values . | this is good information , but is there a way to predict the shape of the graph based on the equation 's characteristics , and without tediously plugging in values for x ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ... | can an exponential growth be used to predict the amount of bacteria cells after a period of time ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so that 's y . this is x . that 's a negative 2 . | is there any relation between log function and e^x ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there . | for example if x=2 and y=25 would the inverse of that happen if the number is negative ( x= -2 and y= 1/5 ) ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | and now we can plot it to see how this actually looks . so let me get some graph paper going here . my x 's go as low as negative 2 , as high as positive 2 . | how can i get the roots of a quadratic function ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so let 's make that my y-axis . and my x values , this could be negative 2 . actually , make my y-axis keep going . | does the same method apply for more complicated functions like y = 1000 x 2^-0.04t ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | now let 's do this point here in orange , negative 1 , 1/5 . negative 1/5 -- 1/5 on this scale is still pretty close . it 's pretty close . | does the constant , `` 5 '' , before the exponent represent the steepness or flatness of the exponential function ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so that 's y . this is x . that 's a negative 2 . | why is x always on the left and y always on the right ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | and now we can plot it to see how this actually looks . so let me get some graph paper going here . my x 's go as low as negative 2 , as high as positive 2 . | so how can you tell if a graph is growing or decaying ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so that 's y . this is x . that 's a negative 2 . | how do you graph functions of e^x ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so that 's y . this is x . that 's a negative 2 . | for exponential functions , does sal have anything with a parent function like y=3^ ( x ) and another problem like y=3^ ( x-1 ) where you have to find the domain and range of each and the horizontal asymptote and the y intercept and if its increasing or decreasing ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | 1/25 is obviously greater than 0 . it 's going to be really , really , really , really , close . now let 's do this point here in orange , negative 1 , 1/5 . | does the rapidly increasing function ever become vertical or really close to vertical ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | this will be my y values . let 's start first with something reasonably negative but not too negative . so let 's say we start with x is equal to negative 2 . | why ca n't b be negative in exponential functions ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ... | how to state domain and range of an exponential function ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | that 's negative 1 . that 's 0 . that is 1 . | is there an exponential curve that contains the given point ( 0,2 ) ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | and let 's do one last value over here . let 's see what happens when x is equal to 2 . then y is 5 squared , 5 to the second power , which is just equal to 25 . | what happens when its a problem like -2 ( 3 ) ^x ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ... | can the speed of the expanding universe be graphed as an exponential function ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | this will be my y values . let 's start first with something reasonably negative but not too negative . so let 's say we start with x is equal to negative 2 . | what would the graph of an exponential function with a negative base look like ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there . | i 'm curious as to what would happen to the point ( 0,1 ) of an exponential eqn : y=2^x when you are given the equation y=-1/4*2^ ( x-4 ) +5 what is the order of executing these steps ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | 2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite . | how do you find the equation of an exponential function from the graph ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so that 's y . this is x . that 's a negative 2 . | for example , if i have 9^x=16 , how can i find the value of `` x '' ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there . | would i plug in let 's say x=0 and solve by saying 4^0-2 -1 4^-3 0 - 2 = - 2 - 1 = -3 f ( x ) =1/64 ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so let me draw it like this . so this could be my x-axis . that could be my x-axis . and then let 's make this my y-axis . | so in this exponential function , the only way the graph will intersect the x-axis or go below it is if the base itself is negative and the domain is an odd integer , correct ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | that 's 0 . that is 1 . and that is positive 2 . | is there any exponential function that does n't intercept the y axis in y = 1 ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | and then finally , we have -- well , actually , let 's try a couple of more points here . let me extend this table a little bit further . let 's try out x is equal to 1 . | however , the area of rain forest is decreasing 20 % each year , and the area of farmland is increasing 20 % each year , complete the table and graph to show the area of each for the next year '' how do you form a table ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | this will be my y values . let 's start first with something reasonably negative but not too negative . so let 's say we start with x is equal to negative 2 . | are exponential functions with negative bases explained or used ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | so that 's y . this is x . that 's a negative 2 . | instead of y = b ^ x can we calculate and plot y = ( -b ) ^ x ? |
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be... | 2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite . | how can we determine if a function is a growth or decay ? |
so ever since i first learned about myosin and actin , there was always this thought that popped in my head , a kind of an analogy , if you will . and for a long time , i thought this analogy was pretty much spot-on . but then , i gave it some more thought . and i realized that i was wrong . and so i 'm going to share ... | and c will be -- i 'll draw it right here at the edge . also , almost no force . and you remember , that this actually falls on a curve that we drew out before . | there would not have been a gradual linear reduction in force after a peak ( as was drawn ) , but rather a long linear increase in force with an abrupt drop to zero once the elastic band had snapped , right ? |
so ever since i first learned about myosin and actin , there was always this thought that popped in my head , a kind of an analogy , if you will . and for a long time , i thought this analogy was pretty much spot-on . but then , i gave it some more thought . and i realized that i was wrong . and so i 'm going to share ... | and that simply means that we did n't have to add any energy . but specifically , the kind of energy we 're talking about is chemical energy . so when people say there 's a passive process , usually in biology , what we 're talking about is not having to use chemical energy . and , of course , in the slingshot example ... | near the end of the video , rishi talks about the `` things '' being active or passive , and he explains that passive does n't involve chemical energy , but then is active just the opposite ( involves chemical energy ) ? |
so ever since i first learned about myosin and actin , there was always this thought that popped in my head , a kind of an analogy , if you will . and for a long time , i thought this analogy was pretty much spot-on . but then , i gave it some more thought . and i realized that i was wrong . and so i 'm going to share ... | and then , i can also , on the x-axis i can put something like , how much i stretched my rubber band . i 'll just put , let 's say , stretch . and then you 'll know that means how much i stretched out the rubber band on my slingshot . | is the sling shot afterall a passive process as it can not stretch on its own ( how about the atp used by our skeletal muscles for the stretch ) ? |
so ever since i first learned about myosin and actin , there was always this thought that popped in my head , a kind of an analogy , if you will . and for a long time , i thought this analogy was pretty much spot-on . but then , i gave it some more thought . and i realized that i was wrong . and so i 'm going to share ... | right ? so you 're converting it all to kinetic energy energy of movement . and when you let go of that stone , it happens automatically . | as in it is chemical energy converted to kinetic energy ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | : let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . | what is screening/shielding effect and how does it effect the atomic radius ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | that 's the nucleus of the other . and they 're sharing electrons . so their electron clouds actually , their electron clouds actually overlap with each other , actually overlap with each other so the covalent bond , there the electrons in that bond could spend some of their time on this atom and some of their time on ... | of electrons and protons , how will the nucleus pull the electrons more closer ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | : let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . | what is the difference between radiation and radioactivity ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | : let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . | ( pm is picometer ) what is correct ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | that 's the nucleus of the other . and they 're sharing electrons . so their electron clouds actually , their electron clouds actually overlap with each other , actually overlap with each other so the covalent bond , there the electrons in that bond could spend some of their time on this atom and some of their time on ... | how many electrons are filled out in each subshell ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | that 's the reason why the smallest atom of all , the element with the smallest atom is not hydrogen , it 's helium . helium is actually smaller than hydrogen , depending on how you , depending on what technique you use to measure it . that 's because , if we take the simplest case , hydrogen , you have 1 proton in the... | why is helium smaller than hydrogen ? |
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent... | that 's the nucleus of the other . and they 're sharing electrons . so their electron clouds actually , their electron clouds actually overlap with each other , actually overlap with each other so the covalent bond , there the electrons in that bond could spend some of their time on this atom and some of their time on ... | why does n't the electrons around the protons push away the outermost electrons ? |
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